An atomic force microscope (AFM) is an apparatus using a probe to perform scanning along the surface of a sample to measure displacement of a cantilever caused by recesses and protrusions on the surface and forming the measured displacement into an image of the surface, thus measuring the surface of the sample on a nano scale. In general, a force is inevitably exerted between two objects (in this case, a probe tip and a sample) arranged in proximity to each other. Thus, since the AFM measures a variation in force caused by recesses and protrusions on the surface of the sample, as the displacement of the cantilever, the AFM in principle imposes no restrictions on the sample. Consequently, the AFM can observe even the structure of an insulator surface which an STM (scanning tunnel microscope) cannot observe.
The accuracy of observation images obtained with the AFM depends on the performance of a feedback controller. With classical control such as PI control that is a conventional control scheme, the relevant frequency band is limited by the resonance frequency of the mechanism. Thus, various efforts have been made to improve the performance of the feedback controller.
For example, the following have been introduced into the control of the AFM in order to allow the z piezo elements in the AFM to be quickly driven: a counter balance method and an active damping method (Non-Patent Document 17 and Non-Patent Document 18), a method of feedforward-compensating information for every shift mode or line (Non-Patent Document 13), and Q value control for a cantilever. However, most of these methods are based on the classical control such as the PI control and implemented in analog circuits (Non-Patent Document 20). Alternatively, an H∞ loop shaping method (Non-Patent Document 21), an adaptive control method (Non-Patent Document 15), and the like may be applied. However, the feedback control system may inevitably be restricted by a Bode's integral theorem.
AFM operation schemes include a contact mode, a non-contact mode, and a tapping mode. The contact mode is based on a contact scheme in which a probe is contacted with the sample surface for scanning. The non-contact mode is based on a non-contact scheme in which the probe is not contacted with the sample surface and the surface topography is measured based on a variation in the oscillation frequency of a cantilever. The tapping mode is based on a periodic contact scheme in which the probe is periodically contacted with the sample surface to measure the surface topography based on a variation in the oscillation amplitude of the cantilever (see Non-Patent Documents 2 and 3). An analysis method for the surface topography based on the contact mode generally controls a piezo Z axis so as to maintain the displacement of the cantilever constant and records a manipulating quantity u(t) for the axis as a surface topography. However, in the analysis method, the relevant frequency band may disadvantageously be limited by the resonant frequency of the mechanism as described above.
Thus, Non-Patent Document 1 proposes a method for estimating the surface of a sample using a disturbance observer (the method is simply referred to as STO). In connection with this control method, Non-Patent Document 1 clarifies that modeling a plant allows the surface topography of an object to be estimated using an estimation mechanism similar to the disturbance observer. Thus, for the STO, the relevant frequency band is not limited by a closed loop. Consequently, the STO is demonstrated to be more advantageous than the conventional method even though the manipulating quantity u(t) does not actually track the surface topography.
In Non-Patent Document 10, hardware is improved to increase the operation speed of the AFM. However, in embodiments according to the present invention described below, control is improved to prevent possible degradation of images obtained with the AFM through high-speed scanning.    [Non-Patent Document 1] “Study of Production and Control of Nano-scale Servo Apparatus for Atomic Force Microscope”, Industrial Instrumentation and Control Workshop of the Institute of Electrical Engineers of Japan, IIC-06-132, p. 1-6 (2006)    [Non-Patent Document 2] “Introduction to Nano-Probe Technique”, Kogyo Chosakai Publishing, Inc. (2001)    [Non-Patent Document 3] “Scanning Probe Microscope”, MARUZEN Co., Ltd.    [Non-Patent Document 4] “Introduction to System Control Theories”, Jikkyo Shuppan Co., Ltd.    [Non-Patent Document 5] “Perfect Tracking Control Method Using Multirate Feedforward Control”, Collection of Papers for the Society of Instrumentation and Control Engineers, 36, p. 766-772 (2000)    [Non-Patent Document 6] “PRO Compensation of Magnetic Disk Apparatus Based on Switching Control and PTC, Industrial Instrumentation and Control Workshop of the Institute of Electrical Engineers of Japan, IIC-04-69, p. 13-18 (2004)    [Non-Patent Document 7] “Harmonic analysis based modeling of tapping mode AFM”, Processings of the American Control Conference, p. 232-236 (1999)    [Non-Patent Document 8] “System Identification for Control Based on MATLAB”, Tokyo Denki University Press (1996)    [Non-Patent Document 9] “Advanced System Identification for Control Based on MATLAB”, Tokyo Denki University Press (2004)    [Non-Patent Document 10] “High-Speed Video Rate AFM”, Instrumentation and Control, Vol. 45, No. 2, p. 99-104 (2006)    [Non-Patent Document 11] “Proposal of Nano-Scale Servo for Atomic Force Microscope Based on Surface Topography Learning with PTC”, Industrial Instrumentation and Control Workshop of the Institute of Electrical Engineers of Japan, IIC-07-52, p. 7-12 (2007)    [Non-Patent Document 12] “Study of Production and Control of Nano-scale Servo Apparatus for Atomic Force Microscope”, Industrial Instrumentation and Control Workshop of the Institute of Electrical Engineers of Japan, IIC-06-132, p. 1-6 (2006)    [Non-Patent Document 13] “Robust Two-Degree-of-Freedom Control of an Atomic Force Microscope”, Asian Journal of Control, Vol. 6, Bo. 2, p. 156-163 (2004)    [Non-Patent Document 14] “Robust Control Approach to Atomic Force Microscopy”, Conf. Decision Contr., p. 3443-3444 (2003)    [Non-Patent Document 15] “On Automating Atomic Force Microcscopes: An Adaptive Control Approach”, Conf. Decision Contr., p. 1574-1579 (2004)    [Non-Patent Document 16] “Digital control of repetitive errors in disk drive system”, IEEE Contr. Syst. Mag., Vol. 10, No. 1, pp. 16-20 (1990)    [Non-Patent Document 17] Rev. Sci. Instrum., 76, 053708 (2005)    [Non-Patent Document 18] Proc. Natl. USA. Sci. USA, 98, 12468 (2001)    [Non-Patent Document 19] Phys. Rev. Lett. 90, 046808 (2003)    [Non-Patent Document 20] “Proposal of Surface Topography Observer for Tapping Mode AFM”, IIC-07-119 (2007)    [Non-Patent Document 21] “Robust Control Approach to Atomic Force Microscopy”, Conf. Decision Contr., p. 3443-3444 (2003)    [Non-Patent Document 22] “Proposal of Surface Topography Learning Observer for Contact Mode AFM”, IIC-07-117, p. 7-12 (2007)    [Non-Patent Document 23] “Zero Phase Error Tracking Algorithm for Digital Control”, Trans. ASME, Journal of Dynamic Systems, Measurement, and Control, Vol. 109, p. 65-68 (1987)    [Non-Patent Document 24] “Zeros of sampled system”, Automatica, 20, 1, p. 31-38 (1984)    [Non-Patent Document 25] “Perfect Tracking Control Method Based on Multirate Feedforward Control”, Trans. SICE, Vol. 36, No. 9, p. 766-772 (2000)